Cluster 2

2.In this question your task is again to run the clustering algorithm from lecture, but on a MUCH bigger graph. So big, in fact, that the distances (i.e., edge costs) are only defined implicitly, rather than being provided as an explicit list.

The data set is below.

clustering_big.txt

The format is:

[# of nodes] [# of bits for each node's label]

[first bit of node 1] ... [last bit of node 1]

[first bit of node 2] ... [last bit of node 2]

...

For example, the third line of the file "0 1 1 0 0 1 1 0 0 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1" denotes the 24 bits associated with node #2.

The distance between two nodes u and v in this problem is defined as the Hamming distance--- the number of differing bits --- between the two nodes' labels. For example, the Hamming distance between the 24-bit label of node #2 above and the label "0 1 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 0 1 0 0 1 0 1" is 3 (since they differ in the 3rd, 7th, and 21st bits).

The question is: what is the largest value of k such that there is a k-clustering with spacing at least 3? That is, how many clusters are needed to ensure that no pair of nodes with all but 2 bits in common get split into different clusters?

NOTE: The graph implicitly defined by the data file is so big that you probably can't write it out explicitly, let alone sort the edges by cost. So you will have to be a little creative to complete this part of the question. For example, is there some way you can identify the smallest distances without explicitly looking at every pair of nodes?

<input type=”text” placeholder="Enter answer here">

In [1]:
import pandas as pd
import numpy as np
import time
In [2]:
# get the file path
file2_path = 'clustering_big.txt'
# convert text file to np.array type
clustering_data_big = np.loadtxt(file2_path)
int_clustering_data_big = clustering_data_big.astype(int)
print('int_clustering_data_big: ')
print(int_clustering_data_big)
int_clustering_data_big: 
[[1 1 1 ..., 1 1 1]
 [0 1 1 ..., 1 0 1]
 [0 1 1 ..., 1 0 1]
 ..., 
 [0 0 1 ..., 1 1 0]
 [0 1 1 ..., 0 1 0]
 [1 0 1 ..., 1 1 0]]
In [3]:
# test4 
# v1: array. Hamming distance
# v2: array. Hamming distance
def calc_distance(v1, v2):
    return np.sum(np.logical_xor(v1, v2))

"""
# def a function to get the key by value in dictionary
# d: dictionary
# v: node
def get_create_key_by_value(d, v):
    if len(d.items()) == 0:
        d[v] = [v] 
        return v
    else: 
        for leader, nodes in d.items():
            if v in nodes:
                return leader
            else:
                d[v] = [v] 
                return v
"""

# def a function to get the key by value in dictionary
# d1: dictionary. leader before
# d2: dictionary. leader after
# v: node  
def get_create_leader_by_value(d1, d2, v):
    if len(d1.items()) == 0:
        d1[v] = [v] 
        d2[v] = v
        return v
    else: 
        leader = d2.get(v, 'not exist')
        if leader == 'not exist':
            d1[v] = [v] 
            d2[v] = v
            return v
        else:
            return leader

"""
# test2 can be found before
# c: dictionary. cluster 
# a: key. added value in dict
# d: key. deleted value in dict
def merge_cluster(c, a, d):
    if a == d:
        return
    else:
        if len(c[a]) >= len(c[d]):
            c[a].extend(c[d])
            del c[d]   
        else:
            c[d].extend(c[a])
            del c[a]
"""            

# test2 can be found before
# c1: dictionary. leader before
# c2: dictionary. leader after
# i: node
# k: node
def merge_cluster(c1, c2, i, k):
    # a: leader. 
    # d: leader. 
    a = get_create_leader_by_value(c1, c2, i)
    d = get_create_leader_by_value(c1, c2, k)
    if a == d:
        return
    else:
        if len(c1[a]) >= len(c1[d]):
            for node in c1[d]:
                c2[node] = a
            c1[a].extend(c1[d])
            del c1[d]   
        else:
            for node in c1[a]:
                c2[node] = d
            c1[d].extend(c1[a])
            del c1[a]
In [8]:
# test
test_dict = {}
print(test_dict.items())
# print(get_key_by_value(test_dict, 2))
print(test_dict)
# print(get_key_by_value(test_dict, 3))
print(test_dict)

# test 4 np.logical_xor()
print(np.logical_xor(int_clustering_data_big[0], int_clustering_data_big[1]))
np.sum(np.logical_xor(int_clustering_data_big[0], int_clustering_data_big[1]))
[]
{}
{}
[ True False False False False  True  True False  True False False False
  True  True False False False  True  True False False False  True False]
Out[8]:
9

Note:

following cell code is too slow to run

%%timeit leader_before = {} leader_after = {}

set all spacing of k-clusters i: former node for i in range(len(int_clustering_data_big)-1):

# print i every 5000 
if i % 5000 == 0: 
    print('i: '+str(i))
*j: latter node*
j = i+1
for k in range(j, len(int_clustering_data_big)):
    # print k every 5000
    if k % 5000 == 0:
        print('k: '+str(k))
    if calc_distance(int_clustering_data_big[i], int_clustering_data_big[k]) <= 2:
        merge_cluster(leader_before, leader_after, i, k)
    else:
        useless_value_1 = get_create_leader_by_value(leader_before, leader_after, i)
        useless_value_2 = get_create_leader_by_value(leader_before, leader_after, k)
*print i and k before new i*
print('i: '+ str(i)+' k: '+str(k))
In [ ]:
# test cell
test_dict = dict()
print('test_dict: ')
print(test_dict)

cluster_test = {'unclustered': [x for x in range(10)]}

unclustered_test = cluster_test['unclustered']
clustered_node = dict()

point = unclustered_test.pop(0)
cluster_test[point] = [point]
# print('cluster: ')
# print(cluster)
# print('unclustered: ')
# print(unclustered)

"""    
for former_node in cluster_test[point]: 
    print('former_node: ')
    print(former_node)
    print('cluster[point]: ')
    print(cluster_test[point])
    deleted_list = []
    for latter_node in cluster_test['unclustered']:
        print('latter_node: ')
        print(latter_node)
        print("cluster_test['unclustered']: ")
        print(cluster_test['unclustered'])
        print('distance: ')
        print(calc_distance(int_clustering_data_big[former_node], int_clustering_data_big[latter_node]))
        if calc_distance(int_clustering_data_big[former_node], int_clustering_data_big[latter_node]) <= 10:            
            cluster[point].append(latter_node)
            deleted_list.append(latter_node)
            print('cluster: ')
            print(cluster)
    print('deleted_list: ')
    print(deleted_list)
    for dele_ele in deleted_list:
        del cluster['unclustered'][cluster['unclustered'].index(dele_ele)]
"""                
In [ ]:
# test cell
a= [0]
a.append(1)
print(a)
In [4]:
start_time = time.time()
cluster = {'unclustered': [x for x in range(len(int_clustering_data_big))]} # [0 1 ... 199,999]

while len(cluster['unclustered'])!=0:
    unclustered = cluster['unclustered']
    
    point = unclustered.pop(0)
    cluster[point] = [point]
    # i = 0
    for former_node in cluster[point]: 
        # print('former_node: ')
        # print(former_node)
        # complete_percent = cluster[point].index(former_node) * 1.0 / len(cluster[point])
        # print('position: '+ str(cluster[point].index(former_node))+' , '+'whole length: '+ str(len(cluster[point])))
        # print('complete_percent: '+str(complete_percent))
        deleted_list = []
        for latter_node in cluster['unclustered']:
            if calc_distance(int_clustering_data_big[former_node], int_clustering_data_big[latter_node]) <= 2:            
                cluster[point].append(latter_node)
                deleted_list.append(latter_node)
        #print('deleted_list: ')
        #print(deleted_list)
        for dele_ele in deleted_list:
            del cluster['unclustered'][cluster['unclustered'].index(dele_ele)]
        # print("cluster['unclustered']: ")
        # print('unclustered length with new latter_node: '+ str(len(cluster['unclustered'])))
        print('cluster length: ' + str(len(cluster)))
        print('unclustered length: '+ str(len(cluster['unclustered'])))
        # if len(cluster['unclustered']) % 1000 == 0:
            # print('unclustered length: '+ str(len(cluster['unclustered'])))
            # print('cluster length: ' + str(len(cluster)))
            
    # print('unclustered length with new former node: '+ str(len(cluster['unclustered'])))
# print('cluster: ')
# print(cluster)      
end_time = time.time()
print('time: ' + str(end_time - start_time) + 's ')
print('time: ' + str((end_time - start_time) / 60) + 'min')
print('time: ' + str((end_time - start_time) / 3600) + 'h')
        
cluster length: 2
unclustered length: 199996
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cluster length: 6117
unclustered length: 2
cluster length: 6118
unclustered length: 1
cluster length: 6119
unclustered length: 0
time: 146921.109s 
time: 2448.68515min
time: 40.8114191667h
In [5]:
print('cluster length: ')
print(len(cluster))
cluster length: 
6119